where \(u\)  is the zonal wind in the upper layer, the wind in the lower layer has been assumed small enough to neglect, and \(\)  is a static stability parameter representing the bulk fractional increase in potential temperature from the surface to the tropopause.H00 uses the symbol \(R\)  to denote the planetary Burger number, which elsewhere [1]}, [2]} is used for the thermal Rossby number. To prevent confusion we use the more explicit notation \(\)  for the planetary Burger number and \(\)  for the thermal Rossby number.\(^,\)The tropopause depth \(H\)  is assumed horizontally uniform and identical in the RCE state and in the presence of the large-scale circulation; see [3]} for justification. H00 applies this to the annual-mean Hadley cells by assuming on-equatorial ascent, that the zonal winds are AMC, and that the descending edge is identical to this baroclinic instability onset latitude. Formally, taking \(\approx 0\) , using (REF ) for \(u\)  in (REF ), and taking the small-angle limit yields the original H00 theory for \(\) , which we denote \(_{H00}\) :
\(_{H00}=()^{1/4}.\) 
